GCF of 83/38, 83/69, 31/61, 16/66
Reviewed By : Phani Ponnapalli
Last Updated at : Mar 29,2023
Use our free GCF of Fractions Calculator tool to compute the GCF of 83/38, 83/69, 31/61, 16/66 i.e 1/1759362 easily. The following is the detailed procedure to determine the greatest common factor of fractions 83/38, 83/69, 31/61, 16/66.
Enter two or more fractions separated by "commas"
Ex: 2/3, 5/7 or 3/5, 5/9, 7/3
What is the GCF of 83/38,83/69,31/61,16/66?
Given fractions are 83/38,83/69,31/61,16/66
To find the GCF of fractions, we have to find the GCF of numerator numbers and LCM of denominator numbers. Its formula is given by
GCF of Fraction = Greatest Common Factor of Numerator/Least Common Multiple of Denominators
In the fractions 83/38,83/69,31/61,16/66, numerators are 83,83,31,16
Denominators are 38,69,61,66
The GCF of 83,83,31,16 is 1 .
LCM of 38,69,61,66 is 1759362.
The greatest common factor of 83/38,83/69,31/61,16/66 = [GCF of 83,83,31,16]/[LCM of 38,69,61,66]= 1/1759362
Therefore, the GCF of 83/38,83/69,31/61,16/66 is 1/1759362.
To find the highest common factor of 83,83,31,16, we have to find the factors of both numbers and list the highest common factor.
The factors of 83 are 1, 83
The factors of 83 are 1, 83
The factors of 31 are 1, 31
The factors of 16 are 1, 2, 4, 8, 16
The HCF of 83,83,31,16 is 1.
Lets's calculate GCF of 83,83,31,16
∴ So GCF of numbers is 1 because of no common factors present between them.
Greatest Common Factor of 83,83,31,16 By Matching Biggest Common Factor Method
Now, list down the factors of 83
:1,83
Now, list down the factors of 83
:1,83
Now, list down the factors of 31
:1,31
Now, list down the factors of 16
:1,2,4,8,16
Greatest Common Factor
We found the factors 83,83,31,16 . The biggest common factor number is the GCF number.
So the greatest common factor 83,83,31,16 is 1.
Lets's calculate LCM of 38,69,61,66
| 2 | 38, 69, 61, 66 |
| 3 | 19, 69, 61, 33 |
| 19, 23, 61, 11 |
∴ So the LCM of the given numbers is 2 x 3 x 19 x 23 x 61 x 11 = 1759362
Thus GCF of Fractions = GCF of Numerators/LCM of Denominators = 1/1759362
Therefore, the GCF of Fractions 83/38,83/69,31/61,16/66 is 1/1759362
Least Common Multiple of 38,69,61,66 with GCF Formula
The formula of LCM is LCM(a1,a2,a3....,an) = ( a1 × a2 × a3 × .... × an) / GCF(a1,a2,a3....,an) x common factors(if more than 2 numbers have common factors).
We need to calculate greatest common factor of 38,69,61,66 and common factors if more than two numbers have common factor, than apply into the LCM equation.
GCF(38,69,61,66) = 1
common factors(in case of two or more numbers have common factors) = 6
GCF(38,69,61,66) x common factors =1 x 6 = 6
LCM(38,69,61,66) = ( 38 × 69 × 61 × 66 ) / 6
LCM(38,69,61,66) = 10556172 / 6
LCM(38,69,61,66) = 1759362
GCF of Fractions Calculation Examples
Here are some samples of GCF of Fractions calculations.
FAQs on GCF of Fractions of 83/38, 83/69, 31/61, 16/66
1. What is the HCF of 83,83,31,16?
The HCF of 83,83,31,16 is 1
2. What is the GCF of a fraction?
The GCF of a fraction is defined as the greatest fraction that divides exactly into 2 or more fractions.
3. How to find GCF in Fractions?
Answer: GCF of fractions can be found using the simple formula GCF of Fractions = GCF of Numerators/LCM of Denominators.
4. What is the GCF of Fractions for 83/38, 83/69, 31/61, 16/66?
Answer: GCF of Numerators as per given numbers 83/38, 83/69, 31/61, 16/66 is
GCF of Numerators i.e. for 83,83,31,16 is 1
LCM of denominators i.e. for 38,69,61,66 is 1759362.
Thus, GCF of Fractions is 1/1759362.Finally, GCF of Fractions for 83/38, 83/69, 31/61, 16/66 is 1/1759362.